Properties

Base field \(\Q(\sqrt{-1}) \)
Weight 2
Level norm 14641
Level \( \left(121\right) \)
Label 2.0.4.1-14641.1-d
Dimension 1
CM no
Base-change yes
Sign -1
Analytic rank odd

Related objects

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Base Field: \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).

Form

Weight 2
Level 14641.1 = \( \left(121\right) \)
Label 2.0.4.1-14641.1-d
Dimension: 1
CM: no
Base change: yes 121.2.a.d , 1936.2.a.i
Newspace:2.0.4.1-14641.1 (dimension 10)
Sign of functional equation: -1
Analytic rank: odd

Hecke eigenvalues

The Hecke eigenvalue field is $\Q$.

Norm Prime Eigenvalue
\( 2 \) 2.1 = (\( i + 1 \)) \( 2 \)
\( 5 \) 5.1 = (\( -i - 2 \)) \( 1 \)
\( 5 \) 5.2 = (\( 2 i + 1 \)) \( 1 \)
\( 9 \) 9.1 = (\( 3 \)) \( -5 \)
\( 13 \) 13.1 = (\( -3 i - 2 \)) \( -4 \)
\( 13 \) 13.2 = (\( 2 i + 3 \)) \( -4 \)
\( 17 \) 17.1 = (\( i + 4 \)) \( 2 \)
\( 17 \) 17.2 = (\( i - 4 \)) \( 2 \)
\( 29 \) 29.1 = (\( -2 i + 5 \)) \( 0 \)
\( 29 \) 29.2 = (\( 2 i + 5 \)) \( 0 \)
\( 37 \) 37.1 = (\( i + 6 \)) \( 3 \)
\( 37 \) 37.2 = (\( i - 6 \)) \( 3 \)
\( 41 \) 41.1 = (\( -5 i - 4 \)) \( 8 \)
\( 41 \) 41.2 = (\( 4 i + 5 \)) \( 8 \)
\( 49 \) 49.1 = (\( 7 \)) \( -10 \)
\( 53 \) 53.1 = (\( -2 i + 7 \)) \( -6 \)
\( 53 \) 53.2 = (\( 2 i + 7 \)) \( -6 \)
\( 61 \) 61.1 = (\( -6 i - 5 \)) \( -12 \)
\( 61 \) 61.2 = (\( 5 i + 6 \)) \( -12 \)
\( 73 \) 73.1 = (\( -3 i - 8 \)) \( -4 \)
\( 73 \) 73.2 = (\( 3 i - 8 \)) \( -4 \)
\( 89 \) 89.1 = (\( -5 i + 8 \)) \( 15 \)
\( 89 \) 89.2 = (\( -8 i + 5 \)) \( 15 \)
\( 97 \) 97.1 = (\( -4 i + 9 \)) \( -7 \)
\( 97 \) 97.2 = (\( 4 i + 9 \)) \( -7 \)

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
\( 121 \) 121.1 = (\( 11 \)) \( 1 \)